Rousseeuw and Hubert's conjecture on maximum regression depth

Let $S$ be a set of $n$ points in $d$-dimensional space. The regression depth of a hyperplane is the minimum number of points intersected by the hyperplane as it undergoes a continuous motion from its initial position to vertical. Rousseeuw and Hubert's conjecture. For every $d$-dimensional set of $n$ points, there exists a hyperplane having regression depth

$$\left\lceil\frac{n}{d+1}\right\rceil.$$

The conjecture asks for the higher-dimensional analogue of the optimal planar bound, and is motivated by the relation between regression depth and center-point phenomena. The supplied source does not indicate whether the conjecture has been resolved.